Warning this is difficult reading in places. It requires math which I have put in the footnotes. But try anyway since I have tried to keep the non-math parts on a popular level.
Jeff Tollaksen of the Boston University Physics Department has a good preprint that agrees, more or less , with my independent ideas. Cognitive scientists believe that mind can be explained entirely in terms of classical physics. We do not. Our working hypothesis is that the specifically quantum properties of mental phenomena include:
fundamental reality is non-local in time.
Tollaksen writes:
Different levels of the brain experience quantum superpositions, but at the conscious level, superposition is never experienced.
I find this remark puzzling. I experience superpositions at the conscious level and I am sure you do. Bohm discusses this explicitly. For example, should I buy a new car or not? The state of indecision is a coherent quantum superposition. Did I do that or not? That is also a superposition. What shall I write? The actual punching of the keyboard collapses that wave function, and so on.
For example, at the very least, superposition is significant in various macromolecules. ... A transition from quantum to classical occurs at some level in brain dynamics, and we suggest that the transition occurs at the point of awareness.
In the many-worlds interpretation there is no collapse. However, David Albert shows that a self-measuring system can be aware of it's parallel selves in the other worlds. This certainly fits my personal experience.
In the GRW stochastic theory quantum states spontaneously collapse into eigenstates of position. This may be a quantum gravity effect. The GRW model is rigged so that large numbers of quantum connected particles collapse quickly. GRW concluded that the collapse did not occur until the wavefunction of a particle in a Stern-Gerlach experiment got entangled with the wavefunction of the brain. This fits the late Eugene Wigner's earlier idea.
... the neurophysiological correlate of consciousness is extended through appreciable portions of the brain
This is the signature of a macroscopic quantum state.
Mandel has done a number of nonlinear optical experiments that show collapse of the wavefunction in the absence of a direct physical interaction.
The only traceable change seems to be in the knowledge of the observer.
Mandel wrote:
The quantum state reflects not only what we know about the system but what is in principle knowable.
Mandel's remark echoes the of-quoted remark:
The universe is not only stranger than we imagine. It is stranger than we can imagine.
The interaction-free measurement can be quantum-erased.
Fig 1 shows either a sequence of Stern-Gerlach measurements for an electron or a neutron, or, a sequence of polarization measurements for a photon. A, B and C are observables or filters. We can compute the probability to observe some eigenvalue property of filter C either in case (a) or (b) above. Case (b) does not have the B filter. The probabilities will differ for the two cases.
This difference is interpreted to mean that the actual act of the B measurement changes the outcome at C...
There are three important discrete symmetry transformations in modern physics. Based on this,Tollaksen uses a theorem by Professor Costa De Beauregard which asserts that in case (a) the sum over all intermediate b' is "topological" independent of time order and in which the number of particles can change! For example, B can be first in time. This corresponds to an EPR experiment in which two particles A and C are emitted from the source B.
i.e., we can think about an EPR type experiment, or a delayed choice, or a multiple time/weak measurement ... This virtual sum over b' elucidates the issues of non-separability and observer-participancy.
This requires much more discussion which I hope to do at a later time. It is not obvious!
What about our experience of the flow of time? It has no place in the modern physics of dead matter except in unconvincing appeals to the second law of thermodynamics. Our memory appears, to a first approximation at least, tied to the increase of entropy in a closed system -- except that the universe is not thermodynamically closed since we cannot define an entropy of gravitation properly in the classical general theory of relativity.
We propose that the solution to the paradox of consciousness and the solution to the paradox of time are but two sides of the same coin, two manifestations of the same underlying phenomenon.The time usually dealt with in physics is Schroedinger time, or the mathematical time evident in the mathematical equations governing the evolution of quantum systems. This time is a virtual time for it characterizes the evolution of potentialiities as opposed to the evolution of our world of classical events. The new time suggested below by the ticking of awareness corresponds to the dynamic psychological time that we experience in our conscious experience.
Recently Aharonov proposed a new type of experiment on a quantum system, the protected experiment. This experiment measures the full wavefunction for a single system by avoiding entanglement with a measuring device, and thus avoiding collapse. These proposed experiments suggest a new meaning for the wavefunction. Consider a protected experiment which measures the wavefunction in space over a certain region. Just after this protected experiment, somebody else does the usual strong measurement and observes the whole particle in one place a distance L from the region of the protected measurement.
Huge currents would have to flow from the extended object to the localized particle, and thus there would be frames in which charge is not conserved. Violation of causality can be avoided if the 2-vector theory is adopted because the intermediate description depends on what happens in the future.
In order to resolve this and numerous other problems in the foundations of quantum theory, we propose that it is necessary to describe quantum systems in terms of two state vectors; the usual one evolving from initial conditions (history state), and a new one evolving backwards in time from future boundary conditions (destiny state).
Consider an experiment that occurs within a certain region of space such as a scattering experiment. The incoming particle, in state PSI1, interacts and then evolves into various outgoing states, such as PSI2, PSI3 etc. In a classical system, there is a one-to-one mapping between incoming states and outgoing states, whereas in QM, it is one-to-many. We can thus define a new type of ensemble that has no classical analog, i.e., a pre-selected (PSI1) and post-selected (PSI3) ensemble or the boundary conditions at the beginning and end of an experiment. In figure 3, a system is prepared (pre-selected) at time t1 in an eigenstate |a>of an operator A and post-selected at time t3 in all eigenstate |b> of operator B. This formalism means we evolve |b> backwards in time and evolve |a>) forwards in time: the present quantum state of a system is literally created out of influences both from the past and from the future.
It is important to note that the 2-vector formalism reproduces all the predictions of standard quantum theory. All the fundamental laws of physics are symmetric under time reversal, with the exception of the theory of measurement in quantum mechanics. The 2-vector formalism re-introduces time symmetry into the theory of measurement. This has great importance from a theoretical standpoint.
Furthermore, the 2-vector formalism resolves some of the fundamental paradoxes of quantum physics, namely the non-locality evident in the Einstein-Podolsky-Rosen paradox, Wheeler's delayed choice paradox, and the Lorentz covariance violation of the collapse of the wavefunction. It also helps to explain some new phenomenon discussed below and in the appendices.
3.2 Weak Measurements
One of the physical consequences of this new formalism is a new type of observable, known as the weak measurement. In the 2-vector formalism, the value of an expectation value of an observable <A> generalizes to the weak value of an observable, where PSIfin is a post-selected ensemble, and PSIin is a pre-selected ensemble:
<A>weak = < PSIfin | A PSIin > / < PSIfin | PSIin >
The weak value is a measureable quantity. Consider an ensemble of N particles preselected with the x component of spin Sx = 1/2 and postselected with Sy = 1/2. At an intermediate time t2 a weak measurement will find the total angular momentum in a direction (at an angle of 45 degrees between x and y) to be N/sqrt2 as long as the uncertainty is of the order sqrtN , i.e. ,the measurement is weak. For an individual spin, the component of spin Sx = 1/sqrt2 which is sqrt2 times bigger than the original eigenvalues.
The weak value has actual physical consequences. In cases of interactions that are weak enough, the outcome of the interaction will be the weak value. Thus the existence of weak values is evidence for the existence of the two boundary conditioas during the intermediate time. The weak value possess some fascinating, almost miraculous qualities. First of all, <A>weak is not bounded by the same spectrum as<A> and incompatible operators are simultaneously measureable.
This feature of weak protected measurements allows, according to Aharonov, "quantum time machines" for, unreliable and rare, time travel to past to times before the machine was built! This is unlike the case for traversable wormholes.
However, in any real experiment, the state of the measuring device is not precisely certain. The uncertainty in the measuring device pointer value therefore translates into uncertainty in the measured variable A. However, we show here that the values obtained for the weak measurement demonstrate a remarkable consistency, thereby supporting the 2- vector understanding over and above the standard quantum mechanical error interpretation.Consider a particle in a square well. First a measurement is made of the particle's kinetic energy to an arbitrary precision. Secondly, we perform a measurement attempting to detect the particles in the classically forbidden region. When they are localized outside the well, it is discovered that the corresponding kinetic energy measurement earlier elicits a negative value which is centered around the classical value E - |U|, the total energy E less the (absolute value of the) potential energy U.
Standard quantum theory interprets this measurement of negative kinetic energy as an error of the measuring device, since all the eigenvalues of the kinetic energy operator are positive, that is, it has nothing to do with any property of the particle. However, this type of consistency strongly suggests something much more than a random collection of errors which is the standard interpretation. Furthermore, the spread of kinetic energy values is as expected from the 2 vector interpretation.
What relevance does this have with issues of consciousness? In particular, we analyze an interesting temporal anomaly: instead of post-selecting far from the well, we can measure the kinetic energy again with greater precision. In this case, almost every time the first kinetic energy measurement yields a negative value, the second kinetic energy measurement yields a positive value. Clearly, in this case, we interpret the negative kinetic energy as an error due to the measuring device. However, we could have decided to measure the position far from the well. In this case, the negative kinetic energy is attributed to the particle. The point is that the post-selected measurement is performed after the measurement of negative kinetic energy.
It seems that the cause is after the effect. From an ensemble standpoint, there is no violation of causality. However, from an individual standpoint, there does seem to be a kind of backwards causality. The errors experienced by the measuring device are like whims, i.e- a random decision not based on the past. However, if we make a pact with the future now, then we are creating meaning in the present, i.e., the particle actually does have a negative weak value to its kinetic energy if we perform the correct experiment in the future.
The paper continues with an obscure model of consciousness based on some of Stapp's work that I may come back to at a future time. I quote a few enticing tidbits.
3.4 New Model for ConsciousnessIn this model, we associate objective consciousness with the selecting or creating of destiny states. We define an awareness variable |Omega> to characterize the relevant state of conscious- ness. We restrict this variable to always he in a definite state. That is, it can never be in a superposition of states. It is our experience that we always experience ourselves in a definite state with certainty. We never experience ourselves in a superposition of states.
I find this starting point to be obscure and questionable as I have already stated. Tollaksen associates consciousness with the action of the destiny state as I do but his details are hard to follow in this "Rough Draft". He does mention that Libet's brain experiments at UCSF suggest the correct conclusion that "it is hard to understand how consciousness could have any dynamical control without some kind of temporal nonlocality." He quotes an interesting teleological remark of the late David Bohm's that the ultimate organizing principle for living matter is "in the outcome of the process and not its genetic origin." The obvious place in which the advanced destiny quantum vector shows itself is in the development of the embryo. Tollaksen does show the essential incompleteness of Francis Crick's so-called Astonishing Hypothesis linking consciousness with electrical oscillations in the cortex. In my view, it is the collision between the history and destiny vectors that actualizes potentiality into actuality and that generates qualia and the unity of consciousness. Our qualia is a protected weak self- measurement of the macro wave function of the brain (or rather the Eccle's gates of the brain which are single electrons in the microtubule dimers according to Hameroff).
THE TWO-VECTOR FORMULATION OF QUANTUM MECHANICS:IMPLICATIONS FOR CONSCIOUSNESS, May 29, 1994 Note, quotations from the preprint will be in the html quote format.
By unity of consciousness we mean that the essence of a conscious "event" is lost when we attempt to break it down into a simple aggregate of localized components as classical physics requires.
any such stochastic modification would require interactions outside the light cone
the essential unity of the psychic state ... mirrors the essential unity of its physical counterpart
... PT invariance can be expressed as ... < a' | c' > < - > < c' | a' >, whereas via Stueckelberg-Feynman interpretation, < a' | c' > < - > < a '| c' >* is equivalent to C, thus the Hermitian symmetry ... is equivalent to CPT invariance.
